Discontinuous local semiflows for Kurzweil equations leading to LaSalle's invariance principle for differential systems with impulses at variable times

Autor(es)

Afonso, S. M. ^[1] ; Bonotto, E. M. ^[1] ; Federson, M. ^[1] ; Schwabik, S. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 250, n. 7, p. 2969-3001, APR 1 2011.
• Citações Web of Science: 19

Resumo

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 08/04159-6 - Dinâmica topológica em equações de Kurzweil e aplicações a equações diferenciais funcionais com retardamento
• Beneficiário: Suzete Maria Silva Afonso
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 08/02879-1 - Equações diferenciais funcionais com retardos e impulsos
• Beneficiário: Márcia Cristina Anderson Braz Federson
• Modalidade de apoio: Auxílio à Pesquisa - Regular